Rigorous perturbation bounds for the QX decomposition for centrosymmetric matrices

Official URL: https://dx.doi.org/10.1080/03081087.2025.2464652

Konrad Burnik suggests a structure-preserving (Formula presented.) factorization for centrosymmetric matrices, known as (Formula presented.) factorization. In this article, we obtain the explicit expressions for rigorous perturbation bounds of the (Formula presented.) factorization when the original matrix is perturbed, either norm-wise or component-wise. First, using the matrix-equation approach, weak rigorous perturbation bounds are derived. Then, strong rigorous perturbation bounds are obtained by combining the modified matrix-vector equation approach with the strategy for the Lyapunov majorant function and the Banach fixed-point theorem. The mixed and component-wise condition numbers and their upper bounds are also explicitly expressed. Numerical tests illustrate the validity of the obtained results.